The invention relates to a frequency-modulated digital signal demodulator having a digital quadrature filter with n elements arranged in cascade, each delaying the input signal by a value T.sub.E =1/F.sub.E where F.sub.E is the sampling frequency. A number of channels are arranged in parallel with the cascade arrangement of delay elements, each channel having a multiplier for multiplying by a given coefficient, and a first and a second summing circuit for summing the respective output signals of said multipliers, the output signals of the two summing circuits constituting the quadrature output signals of the filter and being referred to as reference and phase-shifted signals, and, at the output of the filter, a circuit for calculating the instantaneous phase .phi..sub.n of successive signal samples.
An arrangement operating with a calculation circuit of this general type is described in U.S. Pat. No. 3956623.